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  • The minimum distance between any two points  and <img alt="\mathrm{P_2}" src="https://entranc

The minimum distance between any two points \mathrm{P_1} and \mathrm{P_2} while considering point \mathrm{P_1} on one circle and point \mathrm{P_2} on the other circle for the given circles' equations

\mathrm{\begin{aligned} & x^2+y^2-10 x-10 y+41=0 \\ & x^2+y^2-24 x-10 y+160=0 \text { is } \end{aligned}}----

Option: 1

2


Option: 2

0


Option: 3

1


Option: 4

3


Answers (1)

\mathrm{\text { For circle, } x^2+y^2-10 x-10 y+41=0}

\mathrm{\text { Centre } C_1 \equiv(5,5) \text { and radius, } r_1=3}

\mathrm{\text { For circle, } x^2+y^2-24 x-10 y+160=0}

\mathrm{\text { Centre } C_2 \equiv(12,5) \text { and radius, } r_2=3}

\mathrm{C_1 C_2=7>r_1+r_2}

⇒ Circles are separated
 Required minimum possible distance, \mathrm{P_1P_2} = 7 –(3 + 3) = 1

Posted by

Sumit Saini

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